Apparatus Designed and Built by Physicists who have taught in the Advanced Undergraduate Lab
Signal Processor/Lock-In Amplifier
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Modular Architecture
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Multiple "Strategies" for Extracting Signal from Noise
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Compare Lock-In and Amplitude Detection
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Conceptually Transparent Modules
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Noise Generator and Test Signals Built-In
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Low-Noise Preamplifier, Single-Ended or Differential
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Appropriate for Real Physics Experiments
Introduction
The Signal Processor / Lock-In Amplifer was developed to help students understand theprocess of extracting weak signals that are embedded in a noisy environment. It allows them to experiment with a variety of "electronic strategies," as well as to become familiar with some of the uses of phase-sensitive detection. The SPLIA1-A is the antithesis of the modern commercial research lock-in amplifiers. These elegant devices are essentially "black boxes" to the user (student), since they automatically adjust almost all of their parameters to achieve optimum signal-to-noise. They are designed for ease of operation and to achieve optimal signal recovery, but not to make what we call the "electronic strategies" transparent to the user. In short, wonderful as they are, they were obviously not designed for teaching.
TeachSpin has designed the SPLIA1-A specifically for teaching. However, it can also function quite respectably as a "real" signal processor or lock-in amplifier, for real physics experiments.
Instrument
Understanding Extraction of Signal from Noise
The unique design of TeachSpin's Signal Processor/Lock-In amplifier, SPLIA1-A, makes it particularly appropriate for teaching. Nothing is automated!
The modular layout electrically and spatially separates the preamplifier, filter, amplitude and lock-in detectors, low-pass amplifier, phase shifter, reference oscillator, noise generator, and attenuator. All of the interconnections between the modules must be made by the operator using short BNC cables provided with the apparatus. Students easily configure these individual modules in a variety of ways to explore various "strategies" for enhancing the signal-to-noise of weak signals.
In addition, students must manually adjust all the controls on the SPLIA1-A. With this signal processor, students are required to set the appropriate gain levels on various modules and to monitor the signal as it progresses through the instrument. An interesting set of experiments has students examine the signal-to-noise ratio of a particular signal first using the instrument in its amplitude detection (precision rectifier) mode and then using the instrument as a lock-in amplifier. For the same signal they can toggle between these two systems and begin to appreciate the real power of a lock-in amplifier.
Students can explore the basics of signal processing by using a variety of techniques to "massage" known signals from a built-in signal generator. They can set their own challenges by varying the accompanying "noise" with the built-in noise generator.
And with the confidence gained manipulating known signals, they can then use this instrument which has become "theirs" to wrest signal from noise in a wide variety situations.
Experiments
TeachSpin's Signal Processor/Lock-In Amplifier, SPLIA1-A, gives students an opportunity to explore the function of each part of a signal processor and to understand how it contributes to signal-to-noise enhancement. The suggestions below are only the beginning of the many investigations possible. And once the students have become thoroughly familiar with the instrument they can use "their own" lock-in amplifier to extract weak signals from a multitude of experiments including TeachSpin's Faraday Rotation.
The Frequency Response of the Preamplifier
A good place to start might be to have students study the frequency response of the preamplifier as a function of its gain. For this, the modules would be configured as shown in Figure 1.
Figure 1
The results of such measurements are shown in Figure 2. It may come as a surprise to some students that the frequency response of the preamplifier depends upon its gain. This is, however, a common characteristic of many amplifiers.
Figure 2
Exploring the Effects of Filters
The SPLIA1-A has a sophisticated filter that has many applications. It can be used as a low-pass, high-pass, or bandpass filter with variable Q. The most common application of this filter is in bandpass mode, where it reduces the noise into the detector module.
Figure 3a shows the measured frequency response in the bandpass mode with two different values of Q. In Figure 3b, we show the measured phase shifts of the signal through this filter for the two values of Q. These measurements point to important phase stability considerations, which must be accounted for when using high Q filters and lock-in detection.
Figure 3a
Figure 3b
Comparing Filters
This module also has Chebyshev,Butterworth and Bessel types of filters. Examining the
transient responses of these filters helps students to understand their function. Figure 4 shows the response of the Bessel filter (middle trace) and the Chebyshev filter (lower trace) to the square wave input shown on the upper trace.
Figure 4
Looking at Roll-Off Effects
The low-pass amplifier module has both a6db/oct and 12db/oct roll-off, with time constants varying from 0.3 to 10 seconds. The measured response curves for this output amplifier-filter are shown in Figure 5.
Students can study the effects of various time constants on signals that vary with time, such as when sweeping through a magnetic resonance signal. In that case, it is necessary to select a time constant compatible
with the sweep rate, in order to optimize signal-to-noise enhancement, without distorting the signal. Students can also compare the effects of a 6db/oct and a 12db/oct roll-off filter on enhancement for time varying signals.
Figure 5
Comparing Lock-in and Amplitude Detection
A unique feature of the SPLIA1-A is the ability to process a real physical signal (or a test signal) in different ways. In particular, it is useful to compare signal-to-noise enhancement using amplitude detection with lock-in or phase sensitive detection. Figure 6 (on the left) shows the lock-in configuration of the modules while Figure 7 (on the right) shows the amplitude detection architecture.
Figure 6
Figure 7
Figure 8 below is a slow time scan of a test signal which is being detected both by the lock-in (lower trace) and the amplitude detector (upper trace) using the same overall signal bandwidth.
Figure 8
Finding a Known Signal
TeachSpin's instrument even has a built-in noise source, which can be used to create a test signal with variable signal-to-noise ratios. This signal is created by connecting the reference oscillator through the signal attenuator. This allows students to experiment with signal processing before they use the instrument to process a weak signal from any number of real experiments.
This apparatus offers a wide variety of experiments to help students understand the nature of signal processing and develop a mastery of the lock-in detector. Considering the importance and omnipresence of the modern lock-in amplifier in the research labs of all kinds of experimental sciences, especially physics, it seems clear to us at TeachSpin that the SPLIA1-A belongs in every advanced lab. It is affordable; it is essential; it is ready for your advanced, electronics, or instrument laboratory course.
Additional Resources
Specifications
Preamplifier
Input impedance 1 MW
Noise @ 1kHz 9nV/Hz^½
Common Mode Rejection 100 dB
Max Output Voltage ± 10 V
Filter
Input Impedance 5 MW
Max Input Voltage ± 12.5 V
Frequency Range 3Hz - 3kHz
Q Values .577, .707, 1, 2, 5, 10, 20, 50
Detectors
Input Impedance 100 kW
Max Input Voltage ± 12.5 V
Reference Switch Window ± 2 mV
Reference Switching Spikes 50 mV pp. for .5 µs
Low-Pass Filter / Amplifier (Output)
Input Impedance 1 MW
Max Input Voltage ± 12.5 V
Max Output Volatge ± 10 V
Max Output Current ± 3.5 mA
Time Constant .03, .1. .3, 1.0, 3.0, 10 seconds
6 db/oct and 12 db/oct roll-off
DC Offset ± 10 V
Input Offset Voltage 100 µV
Reference Oscillator
Frequency 2.6 to 3.2 kHz
Harmonic Distortion .3% @ 3Hz, .03% > 30 Hz
Max Output Voltage 4Vpp. (sine),
8.8 Vpp. (Square)
Max Output Current 35 mA
Frequency Stability 200 ppm/oC
at HF, 800 ppm/oC at LF end of range
Phase Shifter
Input Impedance 50 kW
Frequency 3 Hz thru 3kHz
Phase Shift 360o
Quadrature Phase Accuracy ± 2o
Max Input Voltage ± 12.5 V
Noise / Attenuator
Input Impedance 1.1 MW
Attenuation 105
Noise Voltage Output Max 1 V rms